Is it possible to export object from Blender with modifiers and use them in external applications?
A modifier uses part of blenders programming to dynamically alter the mesh data. As such they can only be used within blender, though other software may provide ways to get similar results.

The only way to use the results of blenders modifiers in other software is to apply the modifiers before exporting. For a static mesh nothing more than applying the modifier before exporting is needed, many exporters provide an option to do this for you.

For a modifier that generates an animated result, you will need to "bake" the result as a series of meshes for each frame. The .mdd and .pc2 file formats support mesh data that is different for each frame. Alembic is a newer format that supports baked animations, 3dsmax is listed as supporting alembic.

The only difference between exporting to an .obj file and an .mdd file is that the .mdd file contains multiple copies of the mesh for each of it's visual states. Whether exporting a static or animated object, it is a matter of finding a file format supported in both applications that provides a desired result.